Least Common Multiple (LCM) of 100 and 178
The least common multiple (LCM) of 100 and 178 is 8900.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 100 and 178?
First, calculate the GCD of 100 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 178 = 0 remainder 100 |
| 2 | 178 ÷ 100 = 1 remainder 78 |
| 3 | 100 ÷ 78 = 1 remainder 22 |
| 4 | 78 ÷ 22 = 3 remainder 12 |
| 5 | 22 ÷ 12 = 1 remainder 10 |
| 6 | 12 ÷ 10 = 1 remainder 2 |
| 7 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 186 | 10230 |
| 168 and 148 | 6216 |
| 71 and 103 | 7313 |
| 146 and 109 | 15914 |
| 170 and 55 | 1870 |